

A363485


Number of integer partitions of n covering an initial interval of positive integers with more than one mode.


3



0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 3, 1, 2, 6, 5, 3, 8, 4, 8, 11, 13, 9, 17, 17, 19, 25, 24, 23, 44, 35, 39, 54, 55, 63, 83, 79, 86, 104, 119, 125, 157, 164, 178, 220, 237, 251, 297, 324, 357, 413, 439, 486, 562, 607, 673, 765, 828, 901, 1040, 1117, 1220
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OFFSET

0,7


COMMENTS

A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.


LINKS



EXAMPLE

The a(n) partitions for n = {3, 6, 12, 15, 16, 18}:
(21) (321) (332211) (54321) (443221) (4433211)
(2211) (3222111) (433221) (3332221) (5432211)
(22221111) (443211) (4332211) (43332111)
(33222111) (33322111) (333222111)
(322221111) (43222111) (333321111)
(2222211111) (3322221111)
(32222211111)
(222222111111)


MATHEMATICA

Table[If[n==0, 0, Length[Select[IntegerPartitions[n], Union[#]==Range[Max@@#]&&Length[Commonest[#]]>1&]]], {n, 0, 30}]


CROSSREFS

For parts instead of multiplicities we have A025147, complement A096765.
The complement is counted by A363484.
A000041 counts integer partitions, A000009 covering an initial interval.


KEYWORD

nonn


AUTHOR



STATUS

approved



